Optimal noise-shaping DPCM

This paper presents novel results on the optimal design of Noise-Shaping Differential Pulse-Coded Modulation coders. The main contribution resides in the derivation of explicit analytic formulas for the optimal filters and the minimum achievable frequency weighted reconstruction error. A novel aspect in the analysis is the fact that we account for fed-back quantization noise and that we make no restrictions on the order of the filters deployed.

[1]  Graham C. Goodwin,et al.  Fundamental Limitations in Filtering and Control , 1997 .

[2]  Michael T. Orchard,et al.  On the DPCM compression of Gaussian autoregressive sequences , 2001, IEEE Trans. Inf. Theory.

[3]  P. Noll,et al.  Bounds on Quantizer Performance in the Low Bit-Rate Region , 1978, IEEE Trans. Commun..

[4]  R. C. Brainard,et al.  Direct-feedback coders: Design and performance with television signals , 1969 .

[5]  E. N. Protonotarios,et al.  Entropy power loss in linear sampled data filters , 1967 .

[6]  Toby Berger,et al.  Rate distortion theory : a mathematical basis for data compression , 1971 .

[7]  John B. O'Neal.  Bounds on subjective performance measures for source encoding systems , 1971, IEEE Trans. Inf. Theory.

[8]  N. Jayant.  Digital coding of speech waveforms: PCM, DPCM, and DM quantizers , 1974 .

[9]  E. G. Kimme,et al.  Synthesis of optimal filters for a feedback quantization system , 1963 .

[10]  D. Arnstein.  Quantization Error in Predictive Coders , 1975, IEEE Trans. Commun..

[11]  B. Atal,et al.  Predictive coding of speech signals and subjective error criteria , 1979 .

[12]  David L. Neuhoff,et al.  The validity of the additive noise model for uniform scalar quantizers , 2005, IEEE Transactions on Information Theory.

[13]  U. Grenander,et al.  Toeplitz Forms And Their Applications , 1958 .

[14]  Allen Gersho,et al.  Principles of quantization , 1978 .

[15]  K. H. Barratt.  Digital Coding of Waveforms , 1985 .

[16]  J.-H. Lee,et al.  Digital color halftoning , 2005, IEEE Signal Processing Magazine.

[17]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[18]  H. Spang,et al.  Reduction of Quantizing Noise by Use of Feedback , 1962 .

[19]  Robert M. Gray,et al.  Spectral analysis of quantization noise in a single-loop sigma-delta modulator with DC input , 1989, IEEE Trans. Commun..

[20]  P. Noll.  On predictive quantizing schemes , 1978, The Bell System Technical Journal.